Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial

x^{3} – 3x + 1, x^{5} – 4x^{3} + x^{2} + 3x + 1

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm g(x) = x^{3} – 3x + 1, f(x) = x^{5} – 4x^{3} + x^{2} + 3x + 1

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#### Solution

x^{3} - 3x + 1, x^{5} - 4x^{3} + x^{2} + 3x + 1

Since the remainder ≠ 0

Hence x^{3} - 3x + 1 is not a factor of x^{5} - 4x^{3} + x^{2} + 3x + 1

Concept: Division Algorithm for Polynomials

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